Recently removed cassette (10 speed Ultegra 6600) from wheel to give it a good clean - was very methodical and made sure everything (spacers & cogs) got put back exactly in the order they were before they came off. Now it's back together it won't go into the highest gear (smallest cog).

No adjustments were made to anything (limit screws, cables, b screws) at the time, and don't think I was hamfisted enough to knock anything out of whack so can anyone enlighten as to why this may be? And how to fix it? Is it just a matter of adjusting the h limit screw? If so, how would it have become so out of whack like that?

Yes, when you move major parts, you can generally assume you need to check all the things connected to it and tune if necessary. Your case, you took the back wheel off and removed the cassette...that would dictate your rear derailleur and rear brakes need checked.

Why is it that they make adult bikes that'll generally work for 5'9" or above, yet when you pedal these same bikes they only work for someone who is 5'4" or so?

Yup. Double check everything every time you remove something. Try the barrel adjuster first. Sometimes it that easy. Turn it clockwise a 1/2 turn at a time and see if it changes gears. If it does, turn it another 1/4 turn clockwise for good measure.